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I am referring to this paper:-

"A Parameter-Free Generalized Moment Limiter for High- Order Methods on Unstructured Grids " by Michael Yang and Z.J. Wang.

http://dept.ku.edu/~cfdku/papers/AIAA-2009-605.pdf

They have implemented a general limiter which doesn't require any user input. In the process, they have represented the solution in the cell in terms of the average of derivatives (Eqn. 28 of paper). enter image description here

Can someone please explain how was this representation attained. The understanding of this is a quite high priority for me. Please help.

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